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Is it useful to do three Olympic math problems every day?
Let me introduce myself first. I am an Olympic math teacher. I have always opposed the sea tactics.

The understanding of mathematics and the arrangement of thinking are not cultivated by doing many problems, but by training one's thinking ability purposefully and step by step. As a teacher who doesn't know you at all, I have the following suggestions:

Learn logic and philosophy first. If you feel uninterested, you can start with interesting logic and cultivate your logical thinking ability. This is very useful for future study, especially for knowledge above university level. Of course, the same is true of high school. If you have strong logical thinking ability, it will be particularly easy to learn mathematics and physics.

Second, it is much better to read more books, use more brains and exercise thinking ability than to do more problems. Questions can never be wrong. Endless questions will only turn you into a problem-solving machine, and you may not learn real knowledge. When you learn a new knowledge point, you might as well think about it. What ideas do textbooks (or reference books) use to introduce and analyze this knowledge point? When you understand its thinking, you will master the key knowledge points, because textbooks usually point out the mistakes that ordinary people can easily understand, and focus on analysis and introduction. Reading like this often can grasp the key points and difficulties. In fact, the examination questions issued by the examination Committee are often found in these error-prone concepts. As long as you know this way of thinking, you will find that you and the examination Committee are already at the same level.

Third, we can do some topics, such as Olympic Mathematics (I am doing Olympic Mathematics training now). But I object to the practice of asking students to do many questions and recite many formulas and rules. I think it is very important to cultivate a sense of mathematics, but we must never understand the Olympic numbers by asking questions or memorizing empirical formulas. In fact, after finishing a problem, it is very important to understand other methods (mainly to share other people's ideas) and analyze the results of the problem. When you finish a question, look at the answer you have worked out, sometimes it will give you some unexpected surprises. Usually, a lot of new knowledge is hidden in the results. A very clever question may make you suddenly enlightened about some headache math problems. Friends who don't have this experience can't understand why we often laugh about a book or a topic. The enjoyment of mathematical beauty is generally hidden between the lines of textbooks or the results of topics. Especially when a puzzling problem is decomposed and finally found to be so simple, 1+ 1=2, the sense of ease, satisfaction and accomplishment is self-evident.

Keep looking for questions you are interested in, especially those that seem simple but can't be answered by yourself, and then usually study and try to simplify these questions to gain new knowledge and curiosity. . .

Where is the beauty of mathematics? It lies in simplicity in complexity, in impossible possibilities, in unattainable achievements, and in obedience after rebellion. . .

If you have any questions to discuss in the future, you can leave me a message. Math, physics, chemistry, anything. I may not know the answers to many questions, but I can tell you how to find the key to science.